# Index G

• gamma distribution
• incomplete gamma functions
• analytic properties
• applications
• mathematical
• physical
• approximations
• Chebyshev series
• complex variables
• rational
• asymptotic expansions
• error bounds
• exponentially-improved
• for ratios
• Bohr-Mollerup theorem
• computation
• continued fraction
• definition
• duplication formula
• Euler’s integral
• extrema
• asymptotic approximation
• table of
• Gauss’s multiplication formula
• graphics
• inequalities
• infinite products
• integral representations
• for derivatives
• multidimensional
• logarithm
• continued fraction
• convexity
• graphics
• integral representations
• Taylor series
• maxima and minima
• multiplication formulas
• multivariate
• notation
• reciprocal
• analytic properties
• graphics
• Maclaurin series
• zeros
• recurrence relation
• reflection formula
• relations to hypergeometric function
• scaled
• special values
• tables
• Gaunt coefficient
• $\mathit{3j}$ symbol
• Gaunt’s integral
• $\mathit{3j}$ symbol
• Christoffel coefficients (or numbers)
• comparison with Clenshaw–Curtis formula
• eigenvalue/eigenvector characterization
• for contour integrals
• Gauss–Chebyshev formula
• Gauss–Hermite formula
• Gauss–Jacobi formula
• Gauss–Laguerre formula
• generalized
• Gauss–Legendre formula
• logarithmic weight function
• nodes
• tables
• remainder terms
• weight functions
• tables
• Gauss series
• hypergeometric function
• convergence
• Gauss sums
• number theory
• Dirichlet character
• separable
• theta functions
• Gauss’s ${{}_{2}F_{1}}(-1)$ sum
• $q$-analog
• Gauss’s theorem for vector-valued functions
• Gaussian
• nonperiodic
• Gaussian elimination
• back substitution
• forward elimination
• iterative refinement
• multipliers
• partial pivoting
• pivot (or pivot element)
• residual vector
• triangular decomposition
• tridiagonal systems
• of matrix argument
• applications
• asymptotic approximations
• basic properties
• case $m=2$
• computation
• confluent form
• definition
• Gauss formula
• integral representation
• Jacobi form
• notation
• partial differential equations
• reflection formula
• transformations of parameters
• Gaussian noise
• Lambert $W$-function
• Gaussian polynomials
• definition
• tables
• Gaussian probability functions
• Gaussian unitary ensemble
• Painlevé transcendents
• Gegenbauer function
• definition
• relation to associated Legendre functions
• relation to hypergeometric function
• Gegenbauer polynomials
• Bessel functions
• modified Bessel functions
• general elliptic integrals
• reduction to basic elliptic integrals
• reduction to Legendre’s elliptic integrals
• reduction to symmetric elliptic integrals
• general orthogonal polynomials
• complete
• computation
• continued fractions
• difference operators
• discriminant
• Favard’s theorem
• inequality
• moments
• monic
• monotonic weight function
• Nevai–Blumenthal class
• on countable point sets
• on general sets
• on intervals
• orthonormal
• Poisson kernel
• recurrence relations
• sums of products
• Szegő class
• weight functions
• $x$-difference operators
• zeros
• generalizations of elliptic integrals
• generalized Airy functions
• from differential equation
• asymptotic approximations
• definitions
• relation to Bessel functions
• relation to modified Bessel functions
• tables
• from integral representations
• connection formulas
• definitions
• difference equation
• differential equation
• generalized exponential integral
• analytic continuation
• applications
• mathematical
• physical
• approximations
• asymptotic expansions
• exponentially-improved
• large parameter
• large variable
• Chebyshev-series expansions
• computation
• continued fraction
• definition
• derivatives
• further generalizations
• graphics
• inequalities
• integral representations
• Mellin–Barnes type
• integrals
• notation
• of large argument
• principal values
• recurrence relation
• relations to other functions
• confluent hypergeometric functions
• error functions
• incomplete gamma functions
• series expansions
• special values
• tables
• generalized exponentials
• generalized function
• definition
• generalized functions
• distributions
• generalized hypergeometric differential equation
• confluence of singularities
• connection formula
• fundamental solutions
• singularities
• generalized hypergeometric function ${{}_{0}F_{2}}$
• definition
• of large argument
• generalized hypergeometric functions
• analytic continuation
• analytic properties
• applications
• mathematical
• physical
• approximations
• argument unity
• as functions of parameters
• asymptotic expansions
• formal series
• large parameters
• large variable
• small variable
• balanced
• bilateral series
• Dougall’s bilateral sum
• computation
• contiguous balanced series
• contiguous functions
• contiguous relations
• continued fractions
• definitions
• derivatives
• differential equation
• Dixon’s well-poised sum
• Dougall’s bilateral sum
• Dougall’s very well-poised sum
• Džrbasjan’s sum
• expansions in series of
• extensions of Kummer’s relations
• identities
• integral representations
• integrals
• inverse Laplace transform
• Laplace transform
• $k$-balanced
• Kummer-type transformations
• monodromy
• notation
• of matrix argument
• applications
• computation
• confluence
• convergence properties
• definition
• Euler integral
• expansion in zonal polynomials
• general properties
• invariance
• Kummer transformation
• Laplace transform
• Mellin–Barnes integrals
• notation
• Pfaff–Saalschütz formula
• relations to other functions
• Thomae transformation
• ${{}_{3}F_{2}}$ case
• value at $\mathbf{T}=\boldsymbol{{0}}$
• Pfaff–Saalschütz balanced sum
• polynomial cases
• principal branch (value)
• products
• recurrence relations
• relations to other functions
• associated Jacobi polynomials
• Bessel functions
• classical orthogonal polynomials
• Fresnel integrals
• generalized Bessel polynomials
• Hahn class orthogonal polynomials
• Jacobi polynomials
• Kummer functions
• Meijer $G$-function
• modified Bessel functions
• orthogonal polynomials and other functions
• $\mathit{3j},\mathit{6j},\mathit{9j}$ symbols
• Wilson class orthogonal polynomials
• Rogers–Dougall very well-poised sum
• Saalschützian
• terminating
• transformation of variable
• cubic
• very well-poised
• Watson’s sum
• well-poised
• Whipple’s sum
• Whipple’s transformation
• with two variables
• zeros
• generalized hypergeometric series
• generalized integrals
• asymptotic expansions
• generalized logarithms
• applications
• generalized precision
• generalized sine and cosine integrals
• analytic properties
• asymptotic expansions for large variable
• auxiliary functions
• asymptotic expansions for large variable
• integral representations
• computation
• definitions
• general values
• principal values
• expansions in series of spherical Bessel functions
• integral representations
• interrelations
• notation
• power-series expansions
• relation to sine and cosine integrals
• special values
• generating function
• definition
• Genocchi numbers
• table
• genus
• Riemann surface
• geometric mean
• geometric progression (or series)
• geophysics
• spherical harmonics
• Gibbs phenomenon
• sine integral
• Glaisher’s constant
• Glaisher’s notation
• Jacobian elliptic functions
• Goldbach conjecture
• number theory
• Goodwin–Staton integral
• asymptotic expansion
• computation
• definition
• relations to Dawson’s integral and exponential integral
• Bessel functions
• modified Bessel functions
• Gram–Schmidt procedure
• for least squares approximation
• graph theory
• combinatorics
• relation to amplitude ($\operatorname{am}$) function
• relation to $R_{C}$-function